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The Quarterly Journal of Mathematics 2001 52(2):195-216; doi:10.1093/qjmath/52.2.195
© 2001 by Oxford University Press
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Two-Dimensional Measured Laminations of Positive Euler Characteristic

Lee Mosher1 and Ulrich Oertel1

1 Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, New Jersey 07102, USA. E-mail: mosher@andromeda.rutgers.edu E-mail: oertel@andromeda.rutgers.edu

The sphere lemma of A. Connes says that a compact oriented, 2-dimensional measured lamination of positive Euler characteristic has many sphere leaves. The original proof of Connes uses non-commutative geometry. We give a new proof, using branched surface methods borrowed from 3-manifold theory, and some measure theory imported via Rochlin's lemma.


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